# Homework Help: Circular Permutation problem

1. Jun 6, 2009

### dumpman

1. The problem statement, all variables and given/known data
how many ways can 10 people sit around a roundtable if 3 particular people sit together

2. Relevant equations

3. The attempt at a solution
my attempt was (8-1)! x 3!

2. Jun 6, 2009

### tiny-tim

Hi dumpman!
Looks ok to me!

3. Jun 6, 2009

### Dick

That would only be right if you designate 3 particular seats for the 3 particular people to sit in. I think you have a number of choices for those 3 particular seats.

4. Jun 6, 2009

### dumpman

if 3 arent assigned specifically, then the answer is 10C3 x (8-1)! x 3! ?

5. Jun 6, 2009

### HallsofIvy

What you can do is think of those 3 as constituting one person. That is, find the number of different ways of seating 8 people rather than 10, then multiply by 3! for the number of ways to seat those 3 people. Oh, wait, that is (8-1)! 3!, your first answer.

Dick, that does NOT require designating "3 particular seats for the 3 particular people to sit in". Or are you suggesting we should multiply by 7!3! by 8 to allow for those 3 being any one of the original "8" people? I don't believe that is correct.

(I could be wrong, now!)

6. Jun 6, 2009

### Dick

If the question means "order of seating" then I think you are right if 'right' and 'left' partners are distinguishable. If the question means "ways to seat" as in 'the chairs are numbered' then I think I'm right. It is a little ambiguous. I THINK you have to multiply 7!*3! by the number of ways to pick three consecutive chairs in a roundtable. And that's not 10C3, dumpman. They have to be adjacent. But if you think circular rotations are not important you can go with Halls and tiny-tims answer.

Last edited: Jun 6, 2009
7. Jun 7, 2009

### tiny-tim

all seats are equal

Yes, in my experience, "roundtable" questions always mean that the order (clockwise, say) matters, but not the actual seats …

if you're attending a dinner-party, all you're interested in is where you're sitting in relation to everyone else …

on an ordinary table, you could be stuck at the end, which is different, but on a roundtable all seats are equal.